2
Signed Numbers and
Functions
Powers of 10
Copyright © Cengage Learning. All rights reserved.
2.5
Powers of 10
Copyright © Cengage Learning. All rights reserved.
Powers of 10
Multiplying Powers of 10
To multiply two powers of 10, add the exponents as
follows:
10a  10b = 10a + b
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Example 1
Multiply: (102)(103)
Method 1: (102)(103) = (10  10)(10  10  10)
= 105
Method 2: (102)(103) = 102 + 3
Add the exponents.
= 105
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Powers of 10
Dividing Powers of 10
To divide two powers of 10, subtract the exponents as
follows:
10a  10b = 10a – b
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Example 4
Divide:
Method 1:
Method 2:
Subtract the exponents.
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Powers of 10
Raising a Power of 10 to a Power
To raise a power of 10 to a power, multiply the exponents
as follows:
(10a)b = 10ab
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Example 7
Find the power (102)3.
Method 1: (102)3 = 102  102  102
= 102 + 2 + 2
Use the product of powers rule.
= 106
Method 2: (102)3 = 10(2)(3)
Multiply the exponents.
= 106
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Powers of 10
We have stated that 100 = 1. Let’s see why. To show this,
we use the substitution principle, which states that if a = b
and a = c, then b = c.
To divide powers, subtract the exponents.
Any number other than zero divided by
itself equals 1.
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Powers of 10
Therefore, b = c; that is, 100 = 1.
We also have used the fact that
start with
To show this, we
To divide powers, subtract the exponents.
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Powers of 10
For example,
and
In a similar manner, we can also show that
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Powers of 10
For example,
and
Combinations of multiplications and divisions of powers of
10 can also be done easily using the rules of exponents.
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